Motability, which runs a government-backed scheme to provide cars to disabled people, was criticised last month after a connected company, Motability Operations Group, was found to have paid its chief executive £1.7m in the year to 30 September 2017, including a long-term incentive scheme payment of almost £727,000.
The company also has reserves of £2.4bn, its accounts show.
In a joint meeting hosted by the Treasury and Work and Pensions committees, the MPs confirmed they would write to the NAO about the corporate governance arrangements between the charity, company and scheme.
Appearing before the joint committee, Sarah Newton, the minister for disabled people, said the levels of remuneration at Motability Operations were "quite shocking" and welcomed the decision to ask for an NAO inquiry.
Also attending the committee hearing, Neil Johnson, non-executive chair at Motability Operations, said everyone at the company and charity "feels very strongly that the air needs clearing", and Lord Sterling of Plaistow, chair of the Motability charity, told the committee that the charity had itself written to the NAO to request a review.
Johnson defended the company against accusations of excessive pay and said there had been a "robust debate" at board level that led to the long-term incentive plan being withdrawn in 2015.
As the LTIP was a three-year scheme, it would no longer apply from next year, when executive pay would reduce by 20 per cent, Johnson said.
"My responsibility and the responsibility of my board is to put in place a management team that is actually capable of running this business," Johnson said.
Mike Betts, chief executive of Motability, told the committee that he had no role in setting his own pay and the salary was a "reward for success".
Lord Sterling said the charity’s reserves were a defence against fluctuations in the used-car market and risks in the economy.
"I think it was described by the Charity Commission that we were conservative, cautious," he said. "I have always found in my business career that that is the only way you can survive through difficult times."